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Strike-level rhythm

ambiscape rhythm <session-folder> analyzes the rhythm of quasi-periodic pitched sources — swinging or chimed bells, machine cycles, repeated signals — at strike resolution (~20 ms), far below the 1 Hz grid of the standard features. It needs a prior analyze run (it starts from the cached per-minute mean PSD).

Pipeline

  1. Partials — narrowband peaks of the source(s), found by contrasting the mean spectrum of source-active minutes against quiet minutes (rhythm.detect_partials). Active/quiet minutes are auto-detected from 1–2 kHz octave power (2-means threshold) or overridden with --stop.
  2. Streaming pass — one extra pass over the audio storing, per 20 ms frame, the power envelope and pseudo-intensity at each partial plus a broadband onset function (rhythm.partial_pass).
  3. Sources — partials are grouped into sources by correlating their rectified log-envelope derivatives: partials that rise together belong to the same strike stream (rhythm.cluster_partials).
  4. Strikes — adaptive strongest-first onset picking per source, with the separation guard derived from the onset-function autocorrelation (rhythm.acf_structure, rhythm.pick_strikes) so weak between-strike peaks are rejected without a fixed threshold.
  5. Periodicity — the cycle period from a Rayleigh point-process periodogram (resultant length over a period grid, harmonics included for multi-strike cycles), refined near the ACF fundamental to avoid subharmonics; sliding-window period track for drift (rhythm.best_period, rhythm.period_track).
  6. Repetition vs. variation — strikes are folded into phase clusters (rhythm.phase_clusters) and laid on a rigid cycle grid (rhythm.cycle_grid): per-position hit rates, timing SD, slow wander vs. cycle-to-cycle jitter, lag-1 autocorrelation.
  7. Verification — rhythm.rise_spectrum computes the strike-triggered post/pre spectral rise of any stream: a stream whose rise spectrum shows another source's partials is cross-talk, not an independent strike (such clusters are flagged as crosstalk_suspects in rhythm.json). rhythm.strike_doa gives per-stream azimuth/elevation from the pseudo-intensity at the source's own partials.

Output

analysis/rhythm_overview.png (onset tempogram, phase fold, cycle-grid residuals, IOI histograms) and analysis/rhythm.json (per-source partials, period, phase clusters, DOA, per-position variation statistics, plus circular statistics: per-stream phase_stats — R, circular SD, Rayleigh p — and phase_lock, the per-strike relative phase between sources' primary streams; R near 1 with a small circular SD means the sources are mechanically phase-locked).

Swing verification (rhythm.partial_fm)

A genuinely swinging bell Doppler-modulates its partials by a few cents at the swing period; a chimed bell does not. partial_fm tracks a partial's instantaneous frequency and demodulates at the cycle rate against an off-rate control. In the Haarlem case study both bells show cycle-rate FM 20–70x above control (2.4 and 1.3 cents at the nominals) — both bells physically swing, which makes their millisecond phase lock a genuine mechanical-synchronization observation.

Caveats

  • Sources sharing most of their partials (unison bells) will merge into one stream; check crosstalk_suspects and the rise spectra before interpreting phase clusters as physical strikes. Coincident clusters are flagged on both sides — use rise_spectrum on each to decide which one is the real strike (the artifact's rise spectrum shows the other source's partials).
  • Per-partial DOA in reflective environments (street canyons) is frequency-dependent; treat per-source azimuths as sector estimates, not bearings.
  • Everything runs on the W channel except pseudo-intensity (AmbiX ACN W/Y/Z/X, as elsewhere in ambiscape).